Given a differential p-form q in the exterior algebra ⋀^p V^*, its envelope is the smallest subspace W such that q is in the subspace ⋀^p W^* subset ⋀^p V^*. Alternatively, W is spanned by the vectors that can be written as the tensor contraction of q with an element of ⋀^(p - 1) V. For example, the envelope of d x in V = R^2 is W = 〈d/dx〉, and the envelope of d x_1 ⋀d x_2 + d x_3 ⋀d x_4 in V = R^4 is all of V.

decomposable | differential ideal | differential k-form | exterior algebra | vector space | wedge product